Abstract
Owing to advanced manufacturing techniques, it is possible to produce cylindrical single-mode fibres with nearly arbitrary refractive index profiles. For the design of optical fibres automated optimisation schemes have yet to be exploited. We have employed deterministic local, and stochastic global optimisation schemes for the minimisation of a cost function based on dispersion, dispersion slope, macro-bending losses and mode-field diameter, on the space of continuous piecewise linear dopant concentration profiles. For the local schemes (modified and quasi Newton), it appears possible to select a few initial profiles, such that the optimisation results are close to the “global optima” (within 8%), found using global schemes (simulated annealing and differential evolution), while reducing computation times significantly (minutes instead of days). For the local schemes, the cost function gradient is required. Fréchet derivatives are more efficient than finite-difference approximations. A sensitivity analysis provides useful information for manufacturers regarding the required profile accuracy. A comparison of our optimised fibre designs with commercially available optical fibres demonstrates that existing fibres can be improved.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bingle, M., de Hon, B.P., van Stralen, M.J.N.: Electromagnetic modelling and optimisation for the design of single-mode optical fibres. In: 2001 URSI International Symposium of Electromagnetic Theory, vol. 307.2/MN06.20, pp. 515–517. Victoria, CA, 13–17 May 2001
de Hon B.P.: A modal impedance-angle formalism: rigorous proofs for optical fiber mode counting and bracketing. Radio Sci. 38(2), 8013 (2003)
de Hon B.P., Bingle M.: A modal impedance-angle formalism: schemes for accurate graded-index bent-slab calculations and optical fiber mode counting. Radio Sci. 38(2), 8012 (2003)
Dil J.G., Blok H.: Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide. Opt. Quant. Electron. 5, 415–428 (1973)
Fletcher R.: A new low rank quasi-Newton update scheme for nonlinear programming. In: Ceragioli, F., Dontchev, A., Furuta, H., Marti, K., Pandolfi, L. (eds) IFIP International Federation for Information Processing, System Modeling and Optimization, vol 199, pp. 275–293. Springer, Boston (2006)
Fletcher, R., Leyffer, S.: User manual for FilterSQP. University of Dundee Numerical Analysis Report NA/181. http://www-neos.mcs.anl.gov/. April 1998, version1, June 1998, updated March 1999
Gill P.E., Murray W.: Numerical Methods for Constrained Optimisation. Academic Press, London (1974)
Goffe, W., Ferrier, G., Rogers, J.: Global optimization of statistical functions with simulated annealing. J. Econom. 60(1/2), 65–100 (1994). http://www.netlib.org/opt/simann.f/
Hermann W., Wiechert D.U.: Refractive index of doped and undoped PCVD bulk silica. Mat. Res. Bull. 24(9), 1083–1097 (1989)
Kirkpatrick S., Gelatt C.D., Vecchi M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Meyberg K., Vachenauer P.: Höhere Mathematik. Springer, Berlin (1991)
Mishra, S.K.: Global optimization by differential evolution and particle swarm methods: evaluation on some benchmark functions (2006a). http://www.ssrn.com/abstract=933827. Accessed 30 September 2006
Mishra, S.K.: Performance of the barter, the differential evolution and the simulated annealing methods of global optimization on some new and some old test functions (2006b). http://www.ssrn.com/abstract=941630. Accessed 1 November 2006
Nocedal J., Wright S.J.: Numerical Optimization. Springer-Verlag, New York (1999)
Numerical Algorithms Group Ltd.: NAG Fortran Library Mark 20 (2001). http://www.nag.co.uk/
Rahmat-Samii, Y.,Michielssen, E. (eds.): Electromagnetic Optimization by Genetic Algorithms.Wiley Series in Microwave and Optical Engineering. Wiley, New York (1999)
Smink R.W., de Hon B.P., Tijhuis A.G.: Bending loss in optical fibers-a full-wave approach. J. Opt. Soc. Am. B 24(10), 2610–2618 (2007)
Snyder A.W., Love J.D.: Optical Waveguide Theory. Chapman and Hall, London (1977)
Storn R., Price K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global. Optim. 11(4), 341–359 (1997)
Weile D., Michielssen E.: Genetic algorithm optimization applied to electromagnetics: a review. IEEE Trans. Antennas Propag. 45(3), 343–353 (1997)
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Smink, R.W., de Hon, B.P., Bingle, M. et al. Refractive index profile optimisation for the design of optical fibres. Opt Quant Electron 40, 837–852 (2008). https://doi.org/10.1007/s11082-009-9294-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11082-009-9294-1